Exercise 36 Page 215

Explicit equations for arithmetic sequences follow a specific format. a_n= a_1+(n-1) d In this form, a_1 is the first term of the sequence, d is the common difference, and a_n is the nth term. In the given arithmetic sequence, the first term is a_1= 100. Let's observe the other terms to determine the common difference d. 100+ 10 ⟶110+ 10 ⟶120+ 10 ⟶130 + 10 ⟶ ... The common difference is d= 10. By substituting these two values into the explicit equation and simplifying, we can find the formula for this sequence.

a_n=a_1+(n-1)d

SubstituteII

d= 10, a_1= 100

a_n= 100+(n-1)( 10)

Distr

Distribute 10

a_n=100+10n-10

SubTerm

Subtract term

a_n=10n+90

This equation can be used to find any term in the given sequence. To find a_(10), the 10th term in the sequence, we substitute 10 for n.

a_n=10n+90

Substitute

n= 10

a_(10)=10( 10)+90

Multiply

Multiply

a_(10)=100+90

AddTerms

Add terms

a_(10)=190

The 10th term in the sequence is 190.